They are synthesized and used by protein engineers as potential building blocks for biomimetic substrates. The idea is that if you use beta-peptides instead of natural ones, they may similar enough to interact with other proteins, while being different enough to inhibit processes. (an analogy would be a key that is not quite a perfect fit and when you put it in the door, it gets stuck, thereby rendering the door useless.) The same way, a beta-peptide might interact with some disease causing protein in such a way that it ties it up and prevents it from carrying out its natural function.

Another advantage to beta-peptides is that they may be resistant to protein degrading proteins (proteases). As a result, if they are used as drugs in disease therapy, they wont be broken down by the body as quickly as natural peptide products.